Unrecognized Apple ID or password on my Airport Utility. Yet, my laptop and iphone have the right id/password. What's up?

It's coming from your AirPort Base Station's Back to My Mac settings.

AirPort Utility > select your base station > Edit > Base Station tab > Back to My Mac.

Edit any offending entries.

I have this problem also, and editing the Back to my Mac Apple ID entry doesn't fix it.

Using Airport Utility on two AEB and one AEx, I have entered my Apple ID and password in the Base station-> Back to My Mac field. The input verification happened, the green dot appeared next to my Apple ID, I clicked Update and all seemed well.

Then I tried to add my wife's Apple ID to the Back to My Mac field. Clicked the + to add it, entered her AppleID and Password, input verification happened, green dot next to her entry and the prior entry of my Apple ID. Clicked Update.

The AEB crew an error message and showed an amber dot next to its icon in Airport Utility, with a red dot containing the number 1. Clicking this brings up the message Unrecognized Apple ID or Password. Editing the AEB and going to the Back to my Mac input field shows her Apple ID with a red dot and a message saying it's wrong or can't be authenticated.

Separately checking her Apple ID by signing into appleID to manage her ID works perfectly. Her Apple ID and password are correct and authenticated.

What do I have to do to get my airport base stations and express to accept her Apple ID in Back to My Mac?

Running Yosemite with all updates, two airport base stations (not sure of models, but latest Airport Utility works with them) and an Airport Express.

Any help appreciated.

Run into similar problem while add my wife's account the back to Mac setting on Airport Extreme. Any help is greatly appreciated.